Power-factor correction method and circuit and switching power supply

The invention discloses a power-factor correction method. The power-factor correction method comprises the steps that input currents iin and output voltages Vdc are sampled; input voltages Vin are estimated according to the input currents iin and the output voltages Vdc; electric current loop control is carried out, and the waveform phase of the input currents iin is made to follow the waveform phase of the input voltages Vin; voltage loop control is carried out, the reference quantity of the input currents iin is provided for the electric current loop control, and the output voltages Vdc are made to be stable. According to the power-factor correction method, the input currents and the output voltages of a switching power supply are used as the external variable measured values of a state observer, the input voltages of the switching power supply are obtained by adopting the state observer in an estimation mode, the input voltages do not need to be collected, the collecting quantity is reduced, and errors are